In this exercise, you will evaluate the composite function

Let $f(x)=\sqrt{x}$ and $g(x)=x^2-1$. Evaluate the expression given below.

$$g(f(0))$$

Let R be the region in the first quadrant enclosed by $y=x^2$, $y=2+x$, and x=0. Calculate the volume of the solid generated by revolving R about the x-axis by integrating with respect to x.

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. \

$$y=2 x^2, y=0, x=2$$

the $y$-axis

Find the area of the surface obtained by revolving the curve x=sin t, y=cos 2t, for $-\pi / 4 \leq t \leq \pi / 4$, about the x-axis.

Use Theorem 15 to find the torsion of the given curve at a general point and at the point corresponding to t = 0.

$$\mathbf{r}(t)=\left\langle t, \frac{1}{2} t^{2}, \frac{1}{3} t^{3}\right\rangle$$

For each of the following composite functions, find an inner function u=g(x) and an outer function y=f(u) such that y=f(g(x)). Then calculate dy/dx. $y=\tan 5 x^{2}$

Identify the condition in the following diagnoses.
Bullous keratopathy, left eye
main term: __________

1. El médico le aconseja a Lucía que coma queso y tome leche todos los días porque contienen ____. a. comida basura b. calcio c. dulces d. fibra
2. Estoy enfermo(a) cuando ____. a. hago yoga b. tengo fiebre c. hago ejercicio d. tengo sueño
3. Te voy recetar ____ para la tos. a. una gripe b. carbohidratos c. un jarabe d. una aspirina
4. Para evitar los calambres les recomiendo que ____. a. estiren los músculos b. hagan abdominales c. hagan flexiones d. corran rápido
5. Si ____, te aconsejo que hagas yoga. a. estás en la luna b. estás estresado c. haces cinta d. te caes de sueño
6. Doctor, ____ y tengo dolor de cabeza. a. tengo el oído b. me duele el pecho c. me duele la gripe d. estoy en forma
7. Tengo fiebre, cuando ____. a. tengo 39° centígrados b. evito los antibióticos c. tengo calambres d. mantengo mi dieta
8. ¡No aguanto más! significa que ____. a. estás muy contento(a) b. te gusta hacer ejercicio c. tienes energía d. estás muy estresado(a)

$\rule{1cm}{0.4pt}$ is an example of an inflammatory mediator that stimulates chemotaxis. a. Endotoxin $\hspace{2cm}$ c. A fibrin clot b. Serotonin $\hspace{2cm}$ d. Interleukin-2

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line $y=4$.

$$y=\sqrt{3 x}+4, \quad y=4, \quad x=3$$

Find an equation of the tangent line to the given curve at the specified point.

$$y=\frac{1+x}{1+e^{x}}, \quad \left(0, \frac{1}{2}\right)$$

Find an equation of a curve given that it passes through the point $\left(2, \frac{2\sqrt{5}}{3}\right)$ and that the slope of the tangent line to the curve at any point $P(x,y)$ is given by

$$\frac{dy}{dx}=-\frac{4x}{9y}$$

Find the volume of the solid formed by revolving the region bounded by the graphs of the given equations about the x-axis. x = 6 cos θ, y = 6 sin θ

You have six $10 \mathrm { k } \Omega$ resistors. How can you connect them to produce a total equivalent resistance of $1.5 \mathrm { k } \Omega$?